Our main objective is to study the existence and profile of solutions to (REF ) some of whose components can be positive while others change sign. It is reasonable to expect that there will be solutions with sign-changing spikes, i.e., solutions whose sign-changing components look like rescalings of a sign-changing solution to the problem (REF ). The existence of nonradial sign-changing solutions to (REF ) was first established by Bartsch and Willem in [1]} for dimensions \(N=4\)  and \(N\ge 6\) , and by Lorca and Ubilla for \(N=5\)  in [2]}, taking advantage of some symmetry properties of \(\mathbb {R}^N\) . Other solutions of this type were found in [3]}.
